对数正态与正态分布定时截尾寿命试验参数的近似置信域  

Approximate Confidence Region of Parameters for Lognormal and Normal Distribution under Type-I Life Test

作　　者：丁洁玉[1] 叶尔骅[1] 杨纪龙[2] 

机构地区：[1]南京航空航天大学理学院,南京210016 [2]南京师范大学数学系,南京210024

出　　处：《南京航空航天大学学报》2003年第6期682-687,共6页Journal of Nanjing University of Aeronautics & Astronautics

基　　金：航空基础科学基金 ( 96J5 2 0 90 )资助项目

摘　　要：提出了两步法来获得对数正态和正态分布大样本定时截尾寿命试验参数的近似置信域。对数正态分布试验中 ,在试验时间对数和的极限分布的基础上构造了枢轴量。为克服直接从枢轴量的渐近正态性求解参数 μ,σ的联合置信域的困难 ,本文利用 Wolynetz提出的μ的 MLE的近似分布首先得到μ的近似置信区间 ,然后给定置信区间中的每个 μ,通过枢轴量求得 σ的近似置信区间 ,最终获得 μ,σ的联合近似置信域。类似地在正态分布试验中可由总试验时间的极限分布构造枢轴量 ,从而获得参数 μ和 σ的联合近似置信域。随机模拟结果表明 。Two-step-method is presented for constructing the large sample approximate confidence regions for lognormal and normal distribution under type-I life test. For lognormal distribution, the limit distribution of the logarithmic sum of every sample test time is given to construct the pivot. Then based on the approximate distribution of the MLE of μ which was put forward by Wolynetz in 1974, the first step is to obtain the value of μ in every approximate confidence interval, and the second step is to obtain the approximate confidence interval of σ by the pivot with the definite μ. So the associated approximate confidence region of parameters μ and σ can be obtained finally. As to normal distribution, we can get the result similarly; the only difference is that the pivot is based on the limit distribution of total test time. Large numbers of stochastic simulations show that the results are satisfactory.

关 键 词：对数正态与正态分布 定时截尾寿命试验 近似置信区间 工程统计 渐近正态分布 

分 类 号：TB114.3[理学—概率论与数理统计]